Warp Speed Anomalies

Introduction

One of the single most befuddled issues in the whole history of Star Trek is that of the speed of the ships. The original series gave speeds in 'warp factors'; the warp scale was analogous to the Mach scale in use for the then relatively new supersonic aircraft. The idea was a brilliant one, for by using invented units it clouded the actual speed of the ships and thus helped to avoid contradictions with real life speeds and distances.

Although the original series never stated it onscreen, there was an official version of how fast the warp factors in TOS were supposed to be. It is described in 'The Making of Star Trek', a book which describes many aspects of the show's production. According to the book, in the TOS era the speed was equal to the warp factor cubed times light speed. So for example warp 2 was 2 x 2 x 2 = 8 times lightspeed, while warp 4 was 4 x 4 x 4 = 64 times lightspeed. On this scale the Enterprise's top cruise speed of warp 6 equates to 216 times lightspeed, while the dangerous speed of warp 8 was 512 times lightspeed.

In TNG, the scale became a lot more complex. Instead of warp factor cubed, the speed of a ship is given by warp factor to the power of ten over three. So now warp 6 is equal to 6^(10/3) = 392.5 times lightspeed and warp 8 is 8^(10/3) = 1,024 times lightspeed. However, this only works up to warp 9. Beyond that the power which the warp factor is raised by climbs slowly, then more rapidly. The result is that by warp 9.9 the speed is 3,053 times lightspeed, at warp 9.9999 the speed is about 200,000 times lightspeed, and at warp 10 the speed becomes infinite. This scale remained in use throughout TNG, DS9 and Voyager. The latest series, Enterprise, has apparently reverted back to the TOS scale since it is set before Kirk's time.

Unfortunately, the official scales have been violated many times in canonical statements. I will list the more glaring examples below :

The Original Series

Our first example comes from the very first episode ever made, 'The Cage'. This was never broadcast in the original series run, but much of the footage was used in the later double episode 'The Menagerie'. The plot involves Captain Pike in command of the Enterprise; the ship receives a distress signal sent years before by a civilian vessel. On investigating Pike finds that the single survivor has been held captive by aliens who posses powerful telepathic abilities. To lull the crew into a false sense of security, the aliens project a mental image of a camp of Human survivors on the planet. Once captured by the aliens, Captain Pike introduces himself thus :

Pike :

"My name is Christopher Pike. Commander of the space vehicle Enterprise from a stellar group at the other end of this galaxy."

Our galaxy is some 80,000 light years across, so travelling even a fraction of its diameter should take centuries at any warp factor the Enterprise is capable of. One could interpret 'at the other end of the galaxy' as meaning at the other end of the thickness of the galaxy rather than the length, but even this does not solve the problem; the galaxy is a couple of thousand light years thick in the region of Earth, so at the very least this establishes travel over distances of a thousand light years or so - and crossing this would still be a trip of years according to the official TOS scale. In the later episode 'The Cage', Spock seizes control of the Enterprise at Starbase 11 and takes it to Talos. The time for the trip is unclear, but is certainly no more than two days because Spock's court martial occupies the bulk of the journey. However, one could say that Pike's statement is mere hyperbole.

In the episode 'Bread and Circuses', the Enterprise comes across a world which paralleled Earth's early history, but in which the Roman Empire never fell. On approaching the planet for the first time, Chekov is reporting on their time of arrival :

Kirk :

"Mister Spock, assuming that the wreckage drifted at the same speed and direction for the past six years..."

"Only one sixteenth parsec away captain, we should be there in seconds."

It actually takes the ship less than thirty seconds to reach the planet; there are several cuts in this scene, but there is dialogue over them which makes it clear that there are no significant cuts in the timeline of the events. A parsec is about 3.25 light years, so covering one sixteenth of a parsec in thirty seconds equates to about 215,000 times lightspeed! On the official scale for TOS this would be almost warp factor 60, which is many times the Enterprise's stated top warp factor. It's also about equal to the Encyclopedias stated speed for subspace radio, which is TNG Warp Factor 9.9999.

In the episode 'That Which Survives', Kirk leads a landing party down to investigate an unusual planet. While he is occupied, a mysterious force knocks the Enterprise exactly 990.7 light years away from the planet. Spock, in command in Kirk's absence, orders the ship to return in order to rescue Kirk. The time to return is unclear, though it seems to span no more than 24 hours or so judging by events on the planet. Dialogue between Kirk and the landing party indicates that they have no food or water with them and are unable to find any on the planet. The return trip can therefore take no more than a few days at the very most most. Assuming it took 24 hours, this would equate to a speed of 361,853 x lightspeed; according to the official scale covering this distance should take nearly two years even at the top speed of Warp factor 8.

Another problem crops up in 'The Squire of Gothos'. It is established a couple of times in this episode that the Enterprise is 900 light years from Earth. At the normal cruise of Warp 6 it would take over four years - most of the Enterprise's five year mission time - just to get there from Earth, without any stops. Plus the same time to get back, of course.

In 'Arena', a species known as the Gorn attack a Federation outpost and attempt to destroy the Enterprise. After a brief surface battle Kirk leaves a medical contingent on the surface and beams up to pursue the alien vessel, intent on punishing the aliens. The chase is interrupted by the advanced alien Metrones, who force Kirk and the Gorn captain to fight to the death in single combat. Kirk is victorious, but refuses to kill the Gorn because it claims that the outpost had been placed in Gorn space and so it was the Federation that was in the wrong. The Metrones agree to allow both sides try to negotiate a peace and let them go. However, for some reason they then throw the Enterprise some a vast distance through space. Looking at his instruments, Sulu reports :

Sulu :

"Captain, it's impossible but... there's Sirius over there when it should be over there! And Canopus, and Arcanus. We're... all of a sudden we're clear across the galaxy. Five hundred parsecs from where we are. I mean where. I mean-"

As mentioned earlier a parsec is a distance equal to about 3.25 light years, so 500 parsecs is 1,625 light years. Even at the maximum warp factor 8, covering this distance would take more than three years according to the official scale. Yet Kirk orders the ship to return at warp 2 - at which the trip should take over two hundred years! Yet everybody is acting like all they have to do is wander back to Cestus III and pick up their medical teams.

This case hints at a more general problem with the TOS scale. During the series it became clear that warp factors of 4 or more were actually quite rarely used by Federation craft. For instance in 'Friday's Child' it is stated that a freighter can manage a maximum of warp 2, or only 8 times lightspeed. Kirk frequently orders the Enterprise to proceed at Warp 1 or 2, as above; with an average distance between stars of about four or five light years, this would give travel times even between adjacent systems of between six months and five years! Yet we never have any indication that these sorts of journey times are common even for civilian transports, and they certainly are not typical for starships.

Star Trek V

One of the most notorious examples of this kind in all of Star Trek comes in this movie. The Enterprise is sent to solve a hostage situation on the planet Nimbus III, but on arrival the terrorists, led by Spock's half brother Sybok, overpower the Federation officers and take control of the Starship. Sybok has staged the whole incident with this end in mind, and intends to use the ship to find the mythical planet of Sha'ka'ree. The following dialogue concerns the trip :

Chekov :

"Following new course, warp seven."

Sulu :

"Estimating destination in six point seven hours, present speed."

Sybok then makes an announcement to the ship, which Kirk and company see from the Brig. Sybok makes a long winded speech about how many cultures have a local version of Eden, finishing with :

Sybok :

"Our destination is the planet Sha'ka'ree, which lies beyond the great barrier at the centre of the galaxy."

Kirk :

"The centre of the galaxy!"

Spock :

"Where Sha'ka'ree is fabled to exist."

Kirk :

"The centre of the galaxy can't be reached. No ship has ever gone into the great barrier, no probe has ever returned."

It's made abundantly clear that the ship's destination is the centre of the galaxy, and that they will reach this destination in a matter of hours at warp seven.

So during the course of the movie the Enterprise proceeds from Earth to Nimbus III in an unknown time, and then from Nimbus III to the centre of the galaxy in nearly seven hours at warp seven.

In 'First Contact', Picard establishes that the TNG Federation is 8,000 light years across. Even if it was this large at the time of Star Trek V, then the distance between Earth and Nimbus III could be no more than 8,000 light years. Since our planet is located approximately 25,000 light years from the centre of the galaxy, it follows that Nimbus III must be at least 17,000 light years from the centre. So the second leg of the trip, which lasted six hours forty two minutes, took place at a speed of at least 2,537 light years per hour - over twenty million times the speed of light, or TOS warp factor 281!

The Next Generation

The Next Generation had relatively few blatant contradictions to the official warp speed scale, but some did occur. The most notable came in 'The Chase'. In this episode Professor Galen, who taught Picard archaeology years before, comes to the Enterprise-D to offer the Captain the chance to participate in a major new discovery he is about to make. He describes the journey he intends to make as follows :

Galen :

"The Vulcan ship will take us as far as DS4, an Al-Leyan transport is scheduled to arrive at the station three weeks later and they'll take us to Caere and then we'll use the shuttle to get us to Idri VIII, our first stop."

I have marked the course he intends to follow in red on the image below. The upper right point marks Deep Space Four, the upper left point is Caere, and the lower left point is the planet Idri VIII which Galen describes as their 'first stop'. It's worth noting in passing that the Encyclopedia calls the planet 'Indri VIII', yet Galen clearly pronounces it 'Idri VIII'.

Assuming a 40,000 light year radius for the galaxy, Galen is planning to travel at least 30,000 light years to reach Indri VIII! Galen says that if he had a Starship and full diplomatic access he could accomplish his mission in a matter of weeks. When Galen is killed Picard heads off to Indri VIII to complete his mentor's work. He orders the ship to head there at TNG warp factor 7, which should be a speed of 656 times lightspeed. At this speed it would take about forty five years to follow Galen's course, and several decades even to go in a straight line. Yet the ship completes the journey and several subsequent trips within the space of the episode. No specific time span is given for the episode, the Stardate of 'The Chase' is 46731.5 and that of the next episode ('Frame of Mind') is 46778.1, a gap of only 46.6 stardate units, or 17 days. In addition, when Troi tries to stress to Picard the importance of the conference they were heading to before diverting to Indri VII, Picard says he is quite prepared to inconvenience some squabbling delegates for 'a few days'.

Other TNG episodes also have problems. For example in 'Bloodlines', Riker states that it will take the Enterprise-D 20 minutes to travel 300 billion kilometres at Warp 9. This equates to a speed of 833 x c, which is substantially lower than the 1,516 x c official figure for warp 9.

The episode 'Where Silence has Lease', features the E-D being trapped in a mysterious 'hole in space'. An opening leading back to normal space appears 1.3 parsecs (about 4.2 light years) away, and Picard orders the ship to head for it at Warp factor 2. At this speed it would take five months to reach the hole, which seems like a very leisurely escape manoeuvre.

In 'Clues', the Enterprise-D encounters what initially appears to be a wormhole which throws them a distance of 0.54 Parsecs, Riker comments that this is 'nearly a day's travel in thirty seconds'. At warp six, the ships normal cruising speed, the Enterprise would need 1.6 days to cover the distance. An alternative explanation for this one is that Riker worked the time out for Warp 7, which comes to slightly under 24 hours, but this seems to be an odd choice as it is neither the ships normal or maximum cruise speed. However I would class this one as a possible error only.

Another questionable example comes in the early episode '11001001'. In this episode the Enterprise-D is in a Starbase for refit when the antimatter containment systems begin to slowly fail. With only minutes to go until the ship is destroyed, Data announces that he has set the computer to take the ship out away from the nearby inhabited star systems. This could be taken to indicate that he expected the ship to be able to cover a distance of at least several light years in the time remaining, although no specific distances or speed are given.

Voyager

Voyager initially appears to offer the best possible proof that the official scale is indeed accurate. The whole premise of the show is that the Federation ship has been thrown some seventy thousand light years from Earth, and that it was expected to take about seventy years to reach home. Thus Voyager was expected to average about one thousand times lightspeed, which is warp 8 on the TNG scale.

Unfortunately, Voyager many times violated the scale. Most notably, in the episode 'The 37's' the ship discovers that a number of Humans were kidnapped from Earth in 1937 by an alien species. Some of these were left in stasis on a planet in the Delta Quadrant, and the Voyager crew revive several of these. One of them is no less than Amelia Earhart, who is naturally intrigued by the technology of Voyager. The following dialogue takes place on a tour of the bridge :

Earhart :

"How fast?"

Paris :

"Warp nine point nine. In your terms, that about four billion miles a second."

Four billion miles per second translates to over 21,450 times lightspeed. However, according to the Encyclopedia warp speed chart, Warp 9.9 on the TNG scale is 3,053 times lightspeed. So Paris is apparently off by a factor of seven.

In 'Unimatrix Zero', the ship receives a distress call from a source two light years away. Later, Janeway reports that it took them 2 hours to get there. That's about 8,766 times the speed of light - some 60% faster than the ships designed top maximum speed of warp factor 9.975, which is about 5,500 times lightspeed on the official scale. And bear in mind that Voyager isn't often depicted as being able to reach even her designed maximum sustainable warp factor of 9.975, let alone going much faster.

Another interesting facet of Voyager is the ship's course. This is seen in 'Year of Hell, Part I' when the astrometrics lab comes on line. Voyager's point of origin is roughly at the rim of the galaxy, almost directly opposite the Earth's location. From here it is moving along a path which curves significantly to one side, skirting the galactic core. This course is an odd choice, as it adds several thousand light years to the trip compared to a straight line course. Bringing the astrometrics sensors on line was said to have refined the course enough to slash five years from Voyager's journey. Additional navigational information has subsequently saved the crew even more time.

Deep Space Nine

Deep Space 9 tended not to quote distances, speeds and travel times very often so there are relatively few specific problems in this area. But the show did occasionally fall down because it had a tendency in later years to violate its premise of a space station out beyond the frontier of the Federation.

According to Picard in 'Star Trek : First Contact', the Federation is spread across eight thousand light years. Since Humans were one of the founder members, Earth should probably lie more or less towards the centre of Federation territory. So Deep Space Nine should lie anything up to four thousand light years from Earth. At the standard warp 6 cruise this would be a trip of over ten years. Even at warp 9.9, which most Trek ships cannot reach at all let alone hold for any length of time, crossing four thousand light years would take sixteen months. Yet in the crew of DS9 regularly visit Earth in episodes such as 'Homefront' or 'Past Tense'. It's not often clear just how long these jaunts take, but it's a matter of days at the most; certainly not years.

We could assume that Federation expansion has not been very uniform, leading to Earth lying towards the edge rather than the centre, but given the implied travel times we're looking at distances of a few tens of light years at most here. It's entirely possible that the core of the Federation is a small cluster of worlds, with outlying regions thousands of light years away, but if that is so then all the early talk of being 'out on the frontier' rather goes by the wayside.

Enterprise

The newest incarnation of Star Trek turned out to be both the most consistent and least consistent in terms of warp speeds and distances. The pilot episode 'Broken Bow' has several statements concerning the ship's speed :

Archer :

"God, she's beautiful."

Trip :

"And fast. Warp 4.5 next Thursday."

Archer :

"Neptune and back in six minutes."

Warp 4.5 on the TOS cubed scale is 91.125 times lightspeed. The distance between Earth and Neptune varies between about 4,350 million kilometres and 4,650 million kilometres, so the travel time there and back would be between 5.31 and 5.67 minutes. So if we assume Archer was just rounding his number from five and a half to six minutes, this is actually a pretty good figure. The writers clearly did their homework here!

In a later scene the ship is actually in flight and we get the following dialogue :

Archer :

"Bring us to four-four, Lieutenant."

Hoshi :

"There! What do you call that?"

Reed :

"The deflector's sequencing. It's perfectly normal."

T'Pol :

"Perhaps you'd like to go to your quarters and lie down?"

Hoshi :

"Ponfo mirann."

T'Pol :

"I was instructed to speak English during this voyage. I'd appreciate it if you'd respect that."

Archer :

"It's easy to get a little jumpy when you're travelling at thirty million kilometres a second. Should be old-hat in a week's time."

Thirty million kilometres per second is just about one hundred times the speed of light. Which again is in line with the ship doing about Warp 4.5-5. Both quotes are strong evidence that the TOS cubed scale is in use on Enterprise, which makes sense since it is set before Kirk's time. And you can see why I said the Enterprise writers were clearly trying to be consistent here - at least in the pilot, somebody took the time to sit down and work these numbers out. There was a clear desire to get it right.

The first problem regards Kronos, the Klingon home world. When Archer and Trip are discussing the trip to take Klaang back to his people, the following dialogue occurs :

Trip :

"Since when do we have Vulcan Science Officers?"

Archer :

"Since we need Vulcan starcharts to get to Kronos."

Trip :

"So we get a few maps... and they get to put a spy on our ship?"

Archer :

"Admiral Forrest says we should think of her more as a chaperone."

Trip :

"I thought the whole point of this was to get away from the Vulcans."

Archer :

"Four days there, four days back... then she's gone. In the meantime, we're to extend her every courtesy."

So the ship can do approximately one hundred times the speed of light, and expects to reach Kronos in four days. That puts Kronos slightly over one light year from Earth. Yet the nearest star to Earth is about 4.2 light years away.

Then throw in the fact that Enterprise diverts to Rigel on the way to Kronos. Rigel is a real star which is 860 (±80) light years from Earth. At 100 x lightspeed, it should have taken Enterprise some eight years just to get to Rigel, then eight more years to get back to the Klingon homeworld which lay impossibly close to our own solar system. And so the fun begins.

In Terra Nova, we are told the following about the Terra Nova colony :

Archer :

"It was called the Great Experiment. Could humans colonise deep space? They'd already build New Berlin on the Moon, Utopia Planetia on Mars, even a few asteroid colonies, but all within our solar system. When they found an Earth-like planet less than twenty light-years away, it was hard to resist."

Tucker :

"It took them what, nine years to get there?"

Archer :

"Nine years there, nine years back, but they made it."

In actuality the Colonists never came back from the planet, so who knows what that's about. But nine years to cross 20 light years equates to a speed of 2.22 times lightspeed, or Warp 1.3, which fits very well with the idea of pre-Enterprise Earth ships being limited to low warp.

In 'Civilisation', Archer states the following :

Archer :

"Seventy eight light years to get here, our first act is breaking and entering."

Since Enterprise is the only Star Trek series to use actual dates, this is quite helpful to us. The ship launched on or about the 16th April 2151. Civilization is set on 31st July 2151, meaning it's taken them roughly 106 days to get to the planet. So 78 light years in 106 days means they've averaged 268.77 x lightspeed, or Warp 6.45 on the cubed scale. Whups. They really should have made it more like 30 light years at most.

Warp 1.8 would equate to 5.832 times lightspeed on the cubed scale, which would mean about one year between adjacent star systems. Later on :

Travis :

"Even with a warp three engine you'd be able to cut a five year cargo run down to six months. "

Warp 3 on the cubed scale would be 27 times lightspeed. That's 4.63 times faster than the aforementioned Warp 1.8, which means a five year cargo run would be cut to thirteen months, not six. Cutting it to six months would need a Warp 3.88 engine.

"Duvall got his own command? Thank God we're a hundred light years away."

Remember Enterprise launched around 16th April 2151, and the date for this episode is 1st September 2151, so a span of 138 days. To cover a hundred light years in this time the ship would be averaging 264 times lightspeed, or Warp 6.42 on the cubed scale. Looked at the other way, at an average Warp 4.5 they should be only 34 light years from home at this point. So clearly this isn't Archer just rounding his numbers up.

Then in Fusion :

Archer :

"The Arachnid Nebula. Who'd ever have thought I'd get to see it in person. It's less than a light year away. We'll be there in a few hours."

At their maximum of Warp 5, 125 times lightspeed on the cubed scale, it would take Enterprise 2 days, 22 hours, 7 minutes and 40 seconds to cross a light year. Of course Archer said that it was "less than" a light year. If we assume that "a few hours" means it will take them 4 hours to get there, then the nebula would be 0.057 light years away at Warp 5. That's certainly less than a light year... but it's a hell of a lot less than a light year, in fact it's less than a seventeenth of a light year. Archer isn't technically in error here, but it's kind of like saying the house across the street is "less than a mile away". Well yeah, but you'd be more accurate to say it's less than a hundred feet away.

Next up, Detained. Archer and Mayweather are captured and thrown into a prison planet. Enterprise contacts the authorities and asks them for an explanation. We're told how far away the prison is :

Tucker :

"How far?"

Reed :

"Five point two light years. "

Later, after the ship arrives at the prison, one of the other inmates talks about Archer :

Sajen :

"You're placing a lot of trust in people you've only known for three days. For all we know they've been planted here to stage this revolt so Grat would finally have a reason to kill all of us."

Archer :

"We're not working for the Tandarans!"

So the Enterprise has taken, at most, three days to cover the 5.2 light years. That's a speed of 633.1 times lightspeed, which equates to Warp 8.59 on the TOS cubed scale! At their maximum speed of Warp 5, it should have taken them 15 days and 5 hours to cross 5.2 light years.

On to Two Days and Two Nights. Archer chats to a lady friend about where Earth is :

Archer :

"See the bright blue star at the top?"

Keyla :

"Is that your sun?"

Archer :

"No, look just below. The yellow one. Do you see it?"

Keyla :

"It's so faint!"

Archer :

"It's about ninety light years from here."

This episode takes place on 18th February 2152. If we remember, Enterprise launched on or about 16th April 2151, so it's taken 308 days to reach Risa. Ninety light years in that time equates to 107 times lightspeed, or Warp 4.74 on the cubed scale. So that's a little faster than we might expect - the ship would have to be doing almost top speed straight away from Earth for the whole time to make it work. Still, it's about right, and another example where the writers did do the math. Well done!

In Dead Stop, an alien space station creates a meal of Catfish for Commander Tucker. Archer notes :

Archer :

"I doubt there's a catfish within a hundred and thirty light years. "

We don't have a precise date for Dead Stop - the show cut back on giving specific dates this season for some reason (perhaps to stop people like me working out when they got things wrong?). We know that Carbon Creek, two episodes ago, took place on 1st April 2152. Since each season equates to one year, and this season contains 26 episodes, the episodes should be set about two weeks apart. Thus, Dead Stop should take place around the 30th April 2152, 380 days after launch. To cover 130 light years in that time would mean travelling at an average of 125 times lightspeed, or exactly Warp 5 on the cubed scale.

Once again, this means the ship would have to be going flat out straight away from Earth for the entire journey. Since trying to actually hit Warp 5 seriously overstressed the engines in Fallen Hero, this is very unlikely. But again, clearly somebody said "Warp five ship, how far could it have come in this amount of time..." and did the math. Once again, they are making the effort here and the figures do work, if only just.

In Precious Cargo, we are told regarding the Retellian ship :

Archer :

"T'Pol tells me your vessel can't do much better than warp two."

Goff :

"Warp two point two."

And then later...

Archer :

"We've got pretty good long-range sensors, but your ship could be anywhere within a half dozen light years. It'd be a lot easier if we knew your warp frequency!"

Warp 2.2 on the cubed scale is 10.65 times lightspeed. At that speed it would take the ship a little under seven months to cross half a dozen light years. Did they really wait around that long before questioning this guy? No, they did not.

In The Catwalk, and alien examines the Enterprise computers and comments :

Alien Captain :

"These humans. They've travelled over a hundred light years from their homeworld."

This is less than the last "distance from Earth" we got in Dead Stop, which was one hundred thirty light years. So again, a distance that is well within the expected range - and in fact better than the numbers we've had before. Excellent!

Then, in Future Tense, Archer talks to Admiral Forrest on the comm :

Forrest :

"A hundred light years from Earth. You might have solved the greatest missing person case of the century."

Another good reference, well in line with the ship's top speed. It seems like Enterprise has backtracked a little since Dead Stop's one hundred and thirty light years figure; it also seems like they've stopped heading outwards and started to maintain a fairly constant distance, perhaps exploring at right angles to their previous ourward course. Which makes sense.

Ah, but then in The Crossing :

Archer :

"We're a hundred and fifty light years from Earth, Trip."

Well now, that's quite a jump! It's only been two episodes since Forrest said they were a hundred light years away. That should be around a month, and they've covered fifty light years in that time! To do that would require maintaining 600 times lightspeed, or Warp 8.4 on the cubed scale. Even allowing for a longer than usual time gap for the last couple of episodes, this is clearly much more than the ship could have managed in that time. Another whups moment for Enterprise.

Next up, Horizon. Admiral Forrest orders them to make a course change :

Travis :

"This system's almost thirty light years behind us!"

Archer :

"Admiral Forrest assures me it's only a temporary detour."

This "temporary detour" would take the ship some 87 days at Warp 5. That's one hell of a detour!

Next up is Regeneration. A Borgified Earth transport travels away from Earth :

Archer :

"Earth tracking stations spotted the transport leaving orbit at warp three point nine."

Tucker :

"That's impossible. Those transports can't exceed one point four."

Archer :

"I think it's safe to assume these aliens reconfigured the engines using technology from their own ship."

Enterprise is ordered to intercept this ship. Now, the last we heard Enterprise was 150 light years from Earth. But then it made a 30 light year backtrack in Horizon, putting them 120 light years from Earth. If the ship is doing Warp 3.9, that's 59.32 times lightspeed. And so if Enterprise headed back at Warp 5, 125 times lightspeed, that would mean the two ships had a closing speed of 184.32 times lightspeed. So it should take them 238 days to intercept the ship! Does Starfleet really intend Enterprise to spend the next eight months making this intercept?

Of course, since we are dealing with the Borg we might argue that the transport did a small transwarp hop somewhere along the line. And we do later see that the transport is pulling Warp 4.9. But this doesn't really explain the problem - Starfleet and Archer didn't know the ship would upgrade its warp drive still further, and they don't know about Transwarp at all, yet they expected to be able to intercept the ship and never once questioned the time-frame in which he actually did so.

Next up was probably the biggest speed/distance issue Enterprise ever generated - The Expanse. Earth is attacked, and Enterprise is recalled. Archer orders them to head home at Warp 5. No specific journey time is but the ship arrives back home on 24th April 2153. The previous episode, Bounty, gave us a date of 21st March 2153, so Enterprise took an absolute maximum of 34 days to get home. The last specific distance from Earth we had was 120 light years, which we got from the 150 light year figure given in The Crossing minus the 30 light year backtrack in Horizon. For Enterprise to cross 120 light years in 34 days would mean maintaining no less than 1,289 times lightspeed, or Warp 10.88 all the way home - clearly far beyond their capabilities.

But let's be as generous as possible. We were told that the Horizon's 30 year backtrack was a temporary thing but let's suppose that at the start of Horizon, Enterprise's backtrack turned into a general heading towards home. Not to return to Earth as such, but just to kind of scoot off to the side a bit and explore stuff whilst heading generally Earthwards. The date before they turned back was 10th January 2153, so to get home by 24th April 2153 would mean a 150 light year return trip taking 104 days. That's 526 times lightspeed, or Warp 8.08 on the cubed scale. Clearly this is much better... but still, it's a pretty major assumption that the "temporary detour" turned into a direct course back towards Earth at maximum warp. And even then, the trip is still far beyond their actual capabilities. Hell, Kirk's Enterprise couldn't even hold Warp 8 for more than three months!

We're also given the distance from Earth to the Delphic Expanse :

Soval :

"Do you know where these co-ordinates he gave you are?"

Archer :

"At warp five, about a three month trip."

Soval :

"They're inside the Delphic Expanse."

That puts the Expanse border no more than 31.25 light years from Earth.

"Captain's starlog, supplemental. We've been travelling at warp five for seven weeks. The crew is anxious to begin our mission."

So in fact, the co-ordinates they were given were rather inside the Expanse, and the actual border is seven weeks away at Warp 5 - a distance of 11.98 light years if the cubed formula held true. Given that the Expanse border is a field of huge glowing clouds many light years across, it really should be clearly visible in the night sky from Earth. Indeed, given that Soval says it's about two thousand light years across, it should practically fill half the sky from Earth. Yet it doesn't. In fact the clouds aren't even visible from within the Expanse itself!

We go a fair few episodes without mention of speeds and distances, so it's not until Carpenter Street that we get our next number. Daniels transports Archer and T'Pol back to Earth, which makes T'Pol comment :

T'Pol :

"We just travelled ninety light years back to Earth. "

We don't have a date for Carpenter Street, but the episode after next, Proving Ground, is set on 6th December 2153. Since we know that episodes average one every two weeks (to make a season fit a year), then Carpenter Street should be set somewhere around 6th November 2153. Since Enterrpise arrived back home on 24th April 2153 back in The Expanse, then if they set out immediately at that point they have had 226 days to cover the 90 light years. That's a speed of 145.45 times lightspeed, or Warp 5.26 on the cubed scale. And remember, the ship underwent a significant refit when it arrived home, so if anything the journey should have started weeks after 24th April. So this is another nit.

Next up, Doctor's Orders. The ship must cross a dangerous anomaly with the crew unconscious for the trip. Regarding its size, we are told :

Archer :

"How quickly can we get across it?"

T'Pol :

"Less than an hour at warp four."

Warp 4 on the cubed scale is 64 times lightspeed. One hour at that speed makes the anomaly 0.0073 light years across - about light 2.67 hours. But we're then told :

Tucker :

"I don't want to risk going to warp in there. Who knows what kind of effect this disturbance will have on our warp field. We'll be safer sticking to impulse. You'll have to keep us in comas for at least four days."

To go 2.67 hours in four days would mean Enterprise was going to travel at 0.67 times lightspeed on impulse engines. Of course we know impulse engines only go slower than light, and I truly expected them to mess this calculation up. But once again, somebody on the staff did the math and took care to get it right. Well done! This is also, incidentally, one of the few times where it's made clear that impulse allows 'relativistic' speeds, that is speeds in which the effects of relativity are significant. For example the four days the crew experienced at 0.67 c would equate to 5.37 days to an outside observer.

However, later in the episode Phlox (who is awake and running the ship) states to T'Pol (who he is imagining) :

Phlox :

"There's more than a slight discrepancy!"

T'Pol :

"This can't be correct. We're nearly a quarter of a light year from the far edge!"

Phlox :

"At our current rate of speed we won't be out of this for another ten weeks! Autonavigation is still engaged, engines are online, why aren't we through?"

T'Pol :

"The reconfigured space has expanded."

So they're now a quarter light year from the edge, and expect to cover the distance in ten weeks. Unfortunately, crossing 0.25 light years in 70 days equates to 1.3 times lightspeed. So they are doing Warp 1.09, on impulse no less! Such a shame, given that they got it right earlier on. OH well.

Next up, Damage. Degra has sent some co-ordinates to Enterprise. We're told :

Archer :

"How far away are the co-ordinates?"

T'Pol :

"Four light years. We'll need at least warp three to make it in time. It's unlikely that Degra will wait beyond three days. "

But Warp 3 on the cubed scale is 27 times lightspeed; covering four light years at that speed would take 54 days, not three! To do it in three days would mean 487 times lightspeed, or Warp 7.87. This is one of the more egregious errors Enterprise has made.

In The Forgotten, Degra tells Archer where the Xindi Council is located. Archer replies :

Archer :

"This is nearly a dozen light years away. It'll take us weeks to get there. "

And indeed, if the ship can make top speed of Warp 5 by now then it would take just under 5 weeks to cross a dozen light years. Nicely done! Although if it's still limited to Warp 3 it would take more like 23 weeks. Still, the figures do work if we assume the warp drive is back up to scratch.

Once the crew is back home (after a little side trip to 1944), they take some R&R time. Tucker goes with T'Pol to Vulcan, giving us the definitive statement of how far Vulcan is from Earth :

Tucker :

"You're sorry. You brought me sixteen light years just to watch you get married to someone you barely know!"

No time-frame is given, but even the NX-01 would take 47 days to cross 16 light years - and neither NX class is functional at this point. It seems like a rather excessive vacation, 47 days there and another 47 back - three months round trip! In fairness they could have taken a Vulcan ship. Those have been stated to be capable of Warp 6, which on the cubed scale would be 216 times lightspeed, dropping the trip to 27 days either way. Plus however long they spent on Vulcan, of course. It's still a rather long vacation, though. Zero Hour took place on 14th February 2154; we don't get a date for Home, but the following episode, Borderland, takes place on 17th May 2154 - 92 days later. Knocking off a couple of weeks (the average between episodes) would mean 78 days available for the crew to have a break. So it is feasible for T'Pol and Tucker to have a 54 day holiday to Vulcan and back. You could even say they spent several weeks on Vulcan before returning. So nice one Enterprise, it works out once again. Perhaps at this point you see why I said that Enterprise is both the most and least consistent series when it comes to this issue - the show had the courage to give specific dates and times and speeds very often, and it very often does get them right. But then, it often doesn't.

The next datapoint comes up in Daedalus. A visiting scientist prepares to test a new transporter design. Archer's log says :

Archer :

"Captain's Log, supplemental. We're entering an area known as the Barrens. There's not a star system within a hundred light years. Perfect conditions for Emory's test."

Not a star system within a hundred light years. In the previous episode they were at Vulcan. With episodes two weeks apart on average, they would have to have covered a minimum of one hundred light years in two weeks - 2,608.93 times lightspeed, a whopping Warp 13.77 on the cubed scale. You can fudge it a bit by saying the gap from Kir'Shara to Daedalus is longer than the average two weeks, but it doesn't cure the problem - even at Warp 5 the ship should have taken almost ten months to get a hundred light years away.

With the ship at Warp 3.9 and Enterprise at Warp 5, crossing 120 light years should take 238 days.

ENT : The Expanse

Enterprise returns to Earth, a distance of 120 light years. Time 34 days likely, 104 days maximum possible.

Speed of 1,289 x c likely, 526 x c minimum.

At Warp 5, crossing 120 light years should take 350 days.

ENT : Carpenter Street

The ship is said to be 90 light years from Earth after a maximum of 226 days.

Speed of approx. 145 x c.

At Warp 5, crossing 90 light years should take 263 days.

ENT : Doctor’s Orders

The ship is expected to take ten weeks to cover 0.25 light years on impulse.

Speed of 1.3 x c.

At sublight speeds the trip should take at least 3 months. At the speed of 0.67 x c established earlier in the episode, it would take 137 days.

ENT : Damage

The ship is expected to cover 4 light years in three days at Warp 3.

Warp 3 is 487 x c.

Warp 3 should be 27 x c, making the trip take 54 days.

ENT : Daedalus

The ship has covered 100 light years since the last episode.

Speed of 2,600 x c (assuming average episode gap of two weeks).

At Warp 5 it should take 10 months to cross 100 light years.

Some of the above anomalies can be dismissed as rounding errors or simple miscalculations on the part of the characters, but it is clear that this can only be part of the solution. It's simply impossible to explain episodes like 'Arena' or 'Star Trek V' as such mistakes. Yet we can't just cast aside the idea that ships are limited to hundreds of times lightspeed in the normal course of events, because if ships could regularly achieve very high speeds then the whole premise of Voyager would not make sense.

The only way to reconcile this contradiction is to assume that ships are normally bound by the official warp scales, but that they can achieve higher speeds on specific special occasions. So under what circumstances might these extraordinary speeds be achieved?

We have seen in 'That Which Survives' that the Enterprise could reach warp factor 14.1 under extreme duress. This was considered so dangerous that Scotty was saying that the ship was in imminent danger of being destroyed. So it seems improbable that warp factors of 40 or more could be achieved for even one minute in 'Bread and Circuses', nor does it seem credible that Kirk would risk such a dangerous warp factor just to shave off half an hour or so on a routine investigation. And even if we took this unlikely possibility as fact, this would still not explain the fact that high speeds were achieved in 'Star Trek V' without exceeding warp factor 7. So we can safely rule out the idea that starships achieve high speeds just by pushing their engines especially hard. It must be the case that the speed of a given warp factor is not fixed, as the official scales imply, but is in fact variable.

It's possible that the speed of a given warp factor changes over time, so that warp 5 is 125 times lightspeed in the morning and 500 times lightspeed in the afternoon. Or it's possible that it changes with location, so that warp 5 is 125 times lightspeed at the rim of the galaxy and 500 times lightspeed at the core. I tend to favour the latter. We've already seen that there are 'underspace corridors' and 'transwarp conduits'; I would suggest that there are regions of space in which the speed of a given warp factor is much higher or lower than normal. Amongst fans, these areas tend to be called 'warp highways' for obvious reasons.

Since the official scale tends to hold for most of the time, then most areas of space would tend to be 'normal'. In these areas a ship would follow the official scale precisely. Then there would be areas in which warp drive does not perform so well as normal, as seems to be the case in 'Bloodlines'. This area would need to be fairly widespread, or the Enterprise could have simply have skipped off to one side for a few seconds and then proceeded at normal speed.

Finally, we would have areas of space which were far faster than normal the warp highways. Some may give a ship a relatively modest boost, increasing the speed by just a few percentage points or so. Some may boost the speed by a factor of two or three. And then there are those which give ships a real kick; to explain Star Trek V such a highway would extend from Nimbus III to the galactic core and would have boosted the speed of the Enterprise by a factor of about sixty five thousand.

This theory also helps to explain the Voyager course anomaly. We could assume that ship has not chosen a straight line path because it was able to detect some areas skirting the core where warp speeds were better than average. The astrometrics sensors allowed these regions to be better charted, so allowing a faster path to be chosen.

In general, highways would have to be relatively long term features. For example, there would need to be a highway extending along the course Professor Galen chose in 'The Chase'. The planet was first identified in 2340, so this highway has been in existence for at least twenty nine years. The highway extending to the galactic core must also have existed for some time, since Kirk's statements regarding the Great Barrier imply that it has gained a considerable reputation for being impassable. Yet this highway must be gone by the 2370s, or else Voyager would only need to reach the core to be ensured of a fast ride the rest of the way home.

Warp highways could also be one of the reasons why Earth is so influential. Each highway would be a natural route for ships to follow, and any system that happened to lie at a point where several highways crossed would be a natural stopping off point and ﬂtrading centre. That Earth lies on at least one highway is implied by the fact that Enterprise can reach the Klingon home world in only four days, as stated in the pilot episode of Enterprise.

It is not my intention to claim that the writers of Star Trek have warp highways in mind when writing the show. Far from it. In essence, the warp highways theory is just a way of making the speed of any given warp factor pretty much arbitrary. As such it is a pretty elegant theory because it allows us to excuse any mistake the writers make, no matter how blatant!